Trading Bounds for Memory in Games with Counters

Nathanaël Fijalkow (1) , Florian Horn (2) , Denis Kuperberg (3) , Michaa L Skrzypczak

1 University of Oxford
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

We study two-player games with counters, where the objective of the first player is that the counter values remain bounded. We investigate the existence of a trade-off between the size of the memory and the bound achieved on the counters, which has been conjectured by Colcombet and Löding. We show that unfortunately this conjecture does not hold: there is no trade-off between bounds and memory, even for finite arenas. On the positive side, we prove the existence of a trade-off for the special case of thin tree arenas.

Domaines: Théorie et langage formel [cs.FL]

Nathanaël Fijalkow, Florian Horn, Denis Kuperberg, Michaa L Skrzypczak. Trading Bounds for Memory in Games with Counters. 42nd International Colloquium on Automata, Languages, and Programming (ICALP 2015), 2015, Kyoto, Japan. ⟨10.1007/978-3-662-47666-6_16⟩. ⟨hal-02071065⟩